[B._Beckhoff,_et_al.]_Handbook_of_Practical_X-Ray_(b-ok.org).pdf

Characterized by the emission of e particles

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characterized by the emission of e + particles, positrons, and as with β decay, β + decay produces a continuous spectrum. K capture is the capture of an electron from the inner shell (K shell). The nucleus changes its proton number; in the nucleus one proton transforms into the neutron. The nuclear decay can be followed by the emission of gamma radiation, emission of X-rays or internal conversion. Gamma radiation is emitted during transitions of excited nuclei from their nuclear levels to lower lying nuclear levels. The excited nucleus emits one or several photons. Emission of the cascade of photons depends on the existence of intermediate states in the nucleus. The internal conversion process is an alternative process to gamma emission. The excitation energy is transferred to one of the orbital electrons. This electron receives the energy E e given by: E e = E ex E b , (2.1) where E ex is the excitation energy, and E b is the binding energy of the elec- tron. Emission of X-rays can be followed by filling the holes in the atomic
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56 T. ˇ Cech´ ak and J. Leonhardt shells with an electron from higher shells. The energy of emitted photons is given as a difference of the energies of these shells. The energy of emitted photons is a function of the proton number Z . Activity Activity A of a radioisotope source is defined as its rate of decay—the number of disintegration per time unit A = d N d t [Bq] . (2.2) Bq (Becquerel) replaced the older unit of activity Ci (Curie). 1 Ci=3.7 × 10 10 Bq. The number of disintegrations per unit of time is equal d N d t = λN, (2.3) where λ is the decay constant of the radionuclide. Integrating the equation, we obtain the radioactive decay law: N = N 0 e λt , (2.4) where N is the number of nuclei of a given radioisotope after a time t , and N 0 is the number of nuclei for the time t = 0. Half-Life of Sources Half-life T 1 / 2 is defined as the time after which the initial number of radioac- tive nuclei is reduced by one half, i.e., T 1 / 2 = ln 2 λ (2.5) because 1 2 N 0 = N 0 e λt for t = T 1 / 2 . (2.6) For practical purposes the application of radionuclides with a short T 1 / 2 has a disadvantage. Their activity decreases rapidly, and therefore the number of emitted photons also decreases. Energy of Emitted Radiation The energy of gamma radiation or X-rays emitted by the radioactive sources used by XRF can be linear or continuous. Linear spectra are typical of sources if the nuclear decay is followed by emission of gamma rays or X-rays. Contin- uous spectra are typical of sources emitted by the bremsstrahlung radiation produced when fast electrons interact in matter. Part of their energy can be converted into electromagnetic radiation called bremsstrahlung. This process
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2 X-Ray Sources 57 is used to produce bremssstrahlung X-rays from X-rays tubes (see Sect. 2.1).
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